Figure 4.

Optimal joint torque transitions for a low demand on post-contact joint torque magnitude (0.015 N m). For this low level of initial force production (0.385 N), the optimal controller found a solution that produces perfectly vertically aligned fingertip force upon contact. We show 100 uniformly spaced data markers over 60 ms. (a) The magnitude and direction of the joint torque vector. The angle between the joint torque vector before contact and the torque needed for maximal force production anticipatorily switched at approximately 30 ms before contact. The magnitude of the joint torque vector, however, increases only after reorientation of the joint torque vector. This closely resembles our experimental data. (b) A three-dimensional plot of the joint torque trajectory reveals why the torque vector direction changes before the magnitude. The joint torque vector for producing motion first shrinks in magnitude to close to the origin, then it reorients towards the torque vector needed for force production, and finally it increases in magnitude. Note that the three-dimensional plot looks planar (τ₁–τ₂ plane) because τ₃(t)=0 for all of our optimal solutions.